Jules is training for a marathon. She finds that for the first 5 km of her training run, she runs
at a constant speed of x km/h. For the remaining 7 km of her training run, her speed reduces
by 5 km/h. Write an algebraic expression for the total time Jules takes to run 12 km. Recall
that s t
d = .
x * t1 = 5
(x-5) *t2 = 7
so
t1 = 5/x
t2 = 7 / (x-5)
total time = t = 5/x + 7/(x-5)
= 5 (x-5) /(x^2-5x) + 7x / (x^2 - 5x)
= (12x - 25) / (x^2 -5x)
To write an algebraic expression for the total time Jules takes to run 12 km, we need to calculate the time it takes for Jules to run the first 5 km and the time it takes for her to run the remaining 7 km.
Let's start with the first 5 km. The distance is 5 km, and she runs at a constant speed of x km/h. Using the formula s = d/t, where s is the speed, d is the distance, and t is the time, we can rearrange the formula to solve for t:
t = d/s
In this case, the distance d is 5 km and the speed s is x km/h. So, the time it takes for Jules to run the first 5 km is:
t1 = 5/x
Now let's move on to the remaining 7 km. Her speed reduces by 5 km/h, so her speed for this part is (x - 5) km/h. Using the same formula, the time for this part is:
t2 = 7/(x - 5)
To find the total time, we need to add the times for the first and second parts:
Total time = t1 + t2 = 5/x + 7/(x - 5)
So, the algebraic expression for the total time Jules takes to run 12 km is:
Total time = 5/x + 7/(x - 5)